Generating timing sequence for activating resources linked through time dependency relationships

ABSTRACT

A method, and associated computer program product and computer system. A Direct Acyclic Graph (DAG) includes nodes and directed edges. Each node represents a unique resource and is a predefined Recovery Time Objective (RTO) node or an undefined RTO node. Each directed edge directly connects two nodes and represents a time delay between the two nodes. The nodes are topologically sorted to order the nodes in a dependency sequence of ordered nodes. A corrected RTO is computed for each ordered node.

This application is a continuation application claiming priority to Ser.No. 14/271,785, filed May 7, 2014, now U.S. Pat. No. 9,471,379, issuedOct. 18, 2016, which is a continuation to Ser. No. 12/876,368, filedSep. 7, 2010, U.S. Pat. No. 8,793,690, issued Jul. 29, 2014.

FIELD OF THE INVENTION

The preset invention relates generally to the field of resourcemanagement and more particularly to a system method for generating anactivation sequence of resources in consideration of theirinterdependencies and Recovery Time Objective.

BACKGROUND OF THE INVENTION

IT system often deals with resources and their availability. In case ofdisaster, all systems could be off and thus should be reactivated in away to minimize the business impact. Service Level Agreement (SLA),which may for example define how long a system can be off withoutimpacting the business. Once this period ends, the system should be backon. The acceptable elapse time that a resource can be off withoutimpacting the business is generally defined as the Recovery TimeObjective (RTO).

IT Systems are not anymore monolithic. With new technologies, such asService Oriented Architecture, an end-user application uses differentservices provided by other systems and these services also can use otherservices and so on. So, dependencies exist between the end-userapplications and services. These services use also other systems, suchas web-servers, application-servers, databases and so on. This isanother level of dependencies. These intermediate systems must be on toallow the full system to run correctly. This is not only true at theapplication level components but also at the infrastructure level. Thesystems such as the above mentioned (end-user applications, services,databases . . . ) need an infrastructure to run. The infrastructure is acomposition of servers, network, routers, power supply, etc. Each ofthese components is in fact a resource which must be available at acertain moment to respect the business need and these resources arelinked to each other because some resources need others to be fullyoperational.

It is also possible that a resource needs another resource but notimmediately. For example, a resource needs another but only one hourafter its own activation or next Wednesday or the first day of the nextmonth. This means that a dependency delay also exits.

Then it becomes important to find the optimized activation sequence forall resources composing a solution in order to minimize the businessimpact.

The present invention offers a solution to this need.

SUMMARY OF THE INVENTION

The present invention provides a method, and an associated computerprogram product and computer system, for generating a timing sequencefor activating resources linked through time dependency relationships,said method comprising:

providing a first Direct Acyclic Graph (DAG) having a simulation dateand comprising multiple nodes and multiple directed edges, wherein eachnode of the multiple nodes represents a unique resource and is either apredefined Recovery Time Objective (RTO) node comprising a predefinedRTO denoting a maximum elapsed time that the unique resource ispermitted to remain in its current state or an undefined RTO nodecomprising a positive infinite value, wherein the multiple nodescomprise at least two predefined RTO nodes and at least zero undefinedRTO nodes, wherein each directed edge of the multiple direct edgesrepresents a time delay and directly connects two nodes of the multiplenodes in a direction from a predecessor node of the two nodes to asuccessor node of the two nodes, wherein a predecessor resource beingthe unique resource represented by the predecessor node has a timedependency on a successor resource being the unique resource representedby the successor node such that the predecessor resource requires thesuccessor resource to be in the successor resource's target state nolater than a time consisting of the simulation date incremented by thetime delay;

topologically sorting the nodes of the multiple nodes to order themultiple nodes in a dependency sequence of ordered nodes, such that eachnode in the dependency sequence whose unique resource has a timedependency on the unique resource of at least one other node in thedependency sequence is placed in the dependency sequence before eachnode of the at least one other node;

in traversal of the ordered nodes in the dependency sequence, computinga corrected RTO for each ordered node if the dependency sequence as afunction of (i) the predefined RTO of said each ordered node and, foreach predecessor node connected to said each ordered node: (ii) thecorrected RTO of said each predecessor node and (iii) the time delayrepresented by the edge that directly connects said each predecessornode to said each ordered node;

after said computing the corrected RTO for each ordered node,calculating an estimated RTO as a corrected RTO for each ordered noderemaining as an undefined RTO node, said estimated RTO calculated as afunction of: (a) the corrected RTO of each successor node of eachremaining undefined RTO node and (b) the time delay represented by theedge that directly connects each remaining undefined RTO node to saideach successor node; and

reordering the ordered nodes in the dependency sequence according to anascending order of the corrected RTO of the ordered nodes to form anactivation sequence of the multiple nodes defining a time ordering ofactivation of the unique resources represented by the multiple nodes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of a method used in the present invention.

FIG. 2 shows the steps to determine an optimized activation sequence ofresources as a function of their interdependencies and recovery timeobjective, in accordance with embodiments of the present invention.

FIG. 3 depicts a data model used in the present invention.

FIG. 4 depicts different components used in the present invention.

FIG. 5 depicts a resource with its predecessors, in accordance withembodiments of the present invention.

FIG. 6 depicts a resource with its successors, in accordance withembodiments of the present invention.

FIG. 7 depicts an example of input data pertaining to nodes of adirected graph, in accordance with embodiments of the present invention.

FIG. 8 depicts the result of the topological sort of the nodes in FIG.7, in accordance with embodiments of the present invention.

FIG. 9 depicts the result after the calculation of corrected RTO of thenodes in FIG. 7, in accordance with embodiments of the presentinvention.

FIG. 10 depicts the result after the calculation of the estimated RTO ofthe nodes in FIG. 9, in accordance with embodiments of the presentinvention.

FIG. 11 depicts a reordering of the nodes of FIG. 8 through use of thecorrected RTO of the nodes in 10, in accordance with embodiments of thepresent invention.

FIG. 12 depicts a computer system for implementing embodiments of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention are described herein after by way ofexamples with reference to the accompanying figures and drawings. Thefollowing is a short outline of the concepts, components and wordingused in the present description.

Resource is any physical or virtual entity which is in a current stateand could be move to a target state. To move a resource from its currentstate to the target state, the resource could need other resources.Activating a resource means taking an action to move the resource fromthe current state to the target state. A state doesn't mean that aresource can provide a given functionality to its predecessor becausethis can be achieved by dividing a single resource into severalresources, each providing its own functionality. A state means that aresource needs a set of resources to be able to run in the given state.The state of a resource determines the dependency on which the resourceis depending on.

A dependency is a way to describe that a resource needs another resourcebefore having the target state. Dependency has different attributes suchas a dependency time delay. The dependency time delay may be a literalvalue or an expression. The expression can be transformed to a literalvalue using a date as reference. The dependency can be active or notdepending on the target state of its source. A non-active dependency canbe ignored by the method in one embodiment.

A successor of an original resource is a resource needed by the originalresource to move to the target state of the successor resource.

A predecessor of an original resource is a resource which needs theoriginal resource to move to the target state of the original resource.

A source of a dependency: as the dependencies are directed, the sourcedependency is the resource from which the dependency relationshipstarts.

A target of a dependency: as the dependencies are directed, the targetdependency is the resource to which the dependency relationship ends.

An incoming dependency for a resource is a dependency which has theresource as target.

An outgoing dependency for a resource is a dependency which has theresource as source.

A CRON expression means ‘Computer Run On’ expression as defined in thecomputer world. A CRON is commonly a string comprising several fieldsthat represent a set of times.

Delay on a dependency is the time delay that a resource of a predecessorcan wait for the successor of the predecessor to change into thesuccessor's target state. The time can be represented by a literal valueor a CRON expression. CRON expression is used here to represent a timeexpression, but a skilled person in the art could find another way ofrepresenting such expression. If a dependency has a time delay equal tozero, then the dependency is a synchronous dependency (i.e., theresource needs the dependent resource right-away). Otherwise if the timedelay is a positive value, then the dependency is an asynchronousdependency (i.e., the resource can wait for the dependent resource). Adependency time delay can also be negative; for example, resource ‘A’depends on ‘B’, and ‘B’ needs 2 hours to be able to provide the servicerequested by ‘A’. This dependency can be expressed by stating that ‘A’depends on ‘B’ with a time delay of hours. In other words, theapplication ‘B’ should start 2 hours before the RTO of ‘A’. Thedependency time delay is often defined by the functional requirementsand the design of the solution.

State Expression of a dependency is an expression which determines if adependency is active or not.

RTO means Recovery Time Objective. It is the acceptable elapsed timethat a resource can stay at the current state without impacting thebusiness. The time can be defined as a literal value or as a CRONexpression.

A corrected RTO is an RTO that satisfies all RTOs and time delays of itspredecessors recursively.

An estimated RTO is an RTO calculated for a resource where no ‘CorrectedRTO’ was obtained. Different methods can be applied to calculate anestimated RTO. The estimated RTO is usually calculated based on thesuccessors and outgoing dependencies of a resource. This attribute isrepresented in the present invention by a Boolean flag. If the flag isset to true then the corrected RTO attribute contains an estimated RTO;otherwise the corrected RTO contains a corrected RTO based on the RTOgiven by the business.

A simulation date is used to convert a CRON expressed RTO or a timedelay in a literal value. For example if an expression for an RTO isthat “the resource must be ON by next Monday 11:00 AM” and thesimulation date is “Monday 8:00 AM”, the RTO al value is 3 hours. Thus,a simulation date expresses a specified time on a specified date andtherefore is in units of time, so that a simulation date can beincremented by a time delay. Simulation dates may vary and differsimulation dates may be provided by using either a vector of simulationdates or a CRON expression and thus will provide different results.

A graph that is used herein is a directed weighted graph in the sense ofthe graph theory. It is a collection of vertexes representing resourcesand directed edges representing time dependencies. Each edge has avertex as source and a vertex as target. A vertex is also called a“node”. The edges are weighted with the time delay. By convention, theedges are defined as playing the role of ‘dependency’ (e.g., resource R1depends on resource R2) but the opposite role, namely ‘serve,’ couldalso be defined (e.g., resource R2 serves resource R1) without departingfrom the spirit and scope of the present invention. The resources anddependencies are represented by a directed graph where vertices areresources and edges are dependencies. Each resource has a Recovery TimeObjective property and each dependency has a time delay property. If thedelay property is zero, the dependency is synchronous; otherwise thedependency is asynchronous.

A directed graph is called weakly connected if replacing all of itsdirected edges with undirected edges produces a connected undirectedgraph. An undirected graph is called connected if every pair of distinctvertices in the graph can be connected through some path. If a graphcontains multiple weakly connected graphs, the process of the presentinvention is applied to each weakly connected graph separately.

FIG. 1 is a general flow chart of a method used in the presentinvention. In the first step 102, an external format of the graph isdefined. The format may be defined as a table, an XML format, a databaseor any data-model and/or technology that can support a directed graphmodel. In step 104, the external format is called, read and transformedinto an internal computer format (step 106). The internal format maysatisfy a predefined data model as the one shown in FIG. 3. Afterwards,step 108 will determine which dependencies are active or not. Dependingon their source target state and their dependency state expression, thenon-active dependencies are removed from the graph. In the next step110, the process checks if the graph contains a cycle. If yes, theprocess then stops in step 112 as no optimized activation sequence canbe found because there exists a cycle in the graph. A cycle will preventthe possibility to find an activation sequence. If resources are finegrained enough and follow the principle of ‘separation of concerns’ nocycle should be discovered. As known by those skilled in the art, incomputer science, Separation of Concerns (SoC) is the process ofseparating a computer program into distinct features that overlap infunctionality as little as possible.

Going back to step 110, if no cycle exists in the graph then the processcontinues with step 14. In step 114, the different weakly connectedgraphs are searched. Next step 116 is repeated for each simulation dateand each weakly connected graph found in a previous step. Step 116 isfurther detailed with reference to FIG. 2. The results generated arestored in an internal format (step 118). In step 120, the results areconverted into a user friendly format and provided to the end user instep 122 in the form of a table, a graphic, and/or reports.

FIG. 2 details the different steps performed by step 116 of FIG. 1 todetermine an optimized activation sequence of resources as a function oftheir interdependencies and recovery time objective, in accordance withembodiments of the present invention. The method depicted in FIG. 2generates a timing sequence for activating resources linked through timedependency relationships. The method depicted in FIG. 2 provides a firstDirect Acyclic Graph (DAG) having a simulation date and comprisingmultiple nodes and multiple directed edges. The graph representation ofthe DAG is received in an internal computer format (step 202). As perFIG. 1, the process is run for each weakly connected graph for eachsimulation date. Each node of the multiple nodes in the DAG represents aunique resource and is either a predefined Recovery Time Objective (RTO)node comprising a predefined RTO denoting a maximum elapsed time thatthe unique resource is permitted to remain in its current state or anundefined RTO node comprising a positive infinite value. In oneembodiment, the multiple nodes comprise at least two predefined RTOnodes and at least zero (i.e., zero or more) undefined RTO nodes,wherein each directed edge of the multiple direct edges represents atime delay and directly connects two nodes of the multiple nodes in adirection from a predecessor node of the two nodes to a successor nodeof the two nodes. A predecessor resource is the unique resourcerepresented by the predecessor node and has a time dependency on asuccessor resource. The successor resource is the unique resourcerepresented by the successor node such that the predecessor resourcerequires the successor resource to be in the successor resource's targetstate no later than a time consisting of the simulation date incrementedby the time delay.

In step 204, a topological sort is done on the graph. Differentalgorithms may be used to realize this sort operation such as the known‘Kahn’ or ‘depth-first search’ algorithms . . . to name a few of thosethat a skilled person could apply. The topological sort is executed onlyon directed acyclic graphs identified by steps 110 and 114 of FIG. 1.The topological sort issues a sequence of resources ordered in a waythat if a first resource (R1) has a direct or an indirect dependencywith another resource (R2) then R1 will be placed before R2 in thesequence.

In next step 206, an initialization of the corrected RTO value is made.The corrected RTO is initialized with a positive infinite value and theestimated RTO flag is set to false. The positive infinite value will berepresented as the maximum number that the attribute that represents theRTO can get. Often the computer language offers a literal calledMAX_VALUE for a given numerical type. If the current state timestamp isnot defined, it will be set to the earliest date that the system cansupport. This means the resource has always been in this current state.

In step 208 the ‘Corrected RTO’ is computed. This is done by traversingthe resources as sorted during the topologic sort step, and thecorrected RTO is calculated for each resource R as illustrated in FIG.5.

Firstly, the current ‘Corrected RTO’ for all resources R_(i) and R isdetermined, where i denotes a given resource R_(i) being the source of adependency (Ri, R). In other words, R_(i) is one of the predecessors ofR. The current ‘Corrected RTO’ is determined as follows.

If the current ‘Corrected RTO’ is defined (i.e., not equal to a positiveinfinite value), then the ‘Corrected RTO’ is set as the current‘Corrected RTO’.

If the ‘Corrected RTO’ is not defined (i.e., equal to a positiveinfinite value) and if the current state of the resource is not equal tothe target state, then: (i) if the RTO is a literal, then the current‘Corrected RTO’ takes this literal as value; or (ii) if the RTO is aCRON expression, then the current ‘Corrected RTO’ takes the literalvalue calculated based on the CRON expression and the simulation date.

If the ‘Corrected RTO’ is not defined (i.e., equal to a positiveinfinite value) and if the current state of the resource is equal to thetarget state, then the ‘Corrected RTO’ will be set with the differencebetween the current state timestamp and the simulation date.

Secondly, the new ‘Corrected RTO’ is set with a minimum value X_(i)calculated as a function of all resources R_(i) having a dependence on R(R_(i), R) (meaning for all incoming dependencies) and R's current‘Corrected RTO’, wherein X_(i) is the sum of the current ‘Corrected RTO’of the resource R_(i) and the time delay d_(i) of the edge between R_(i)and R. If R current ‘Corrected RTO’ is not the minimum and R has itscurrent state equal to the target state, then an error should be raisedbecause R should be activated earlier to satisfy the new constraint. Ifa resource has no predecessor, such as for the first resource thetopological sort, then as there is no (R_(i), R) dependency and there isno X_(i), and thus the minimum value is the current ‘Corrected RTO’ ofR. If the time delay is a CRON expression, the conversion to a literalvalue is done by calculating the next date using, as base date, the sumof the source resource current ‘Corrected RTO’ and the simulation date.Once the next date is found, the base date is subtracted from the nextdate to find the literal time delay.

Once all Corrected RTOs are computed, if there remains one or moreresource(s) still having an undefined ‘Corrected RTO’, step 210 may beperformed to compute an Estimated RTO for each such resource.

It is to be noted that while an undefined RTO is not recommended, thepresent invention comprises a step to take into consideration such acase having an undefined RTO. An undefined RTO may appear either if theresources are not specified originally by a business entity or if noother resource imposes an RTO on the resources. This may also happenwhen a resource has all its predecessors with an undefined ‘CorrectedRTO’.

Thus in step 208 in traversal of the ordered nodes in the dependencysequence, a corrected RTO is computed for each ordered node in thedependency sequence as a function of (i) the predefined RTO of said eachordered node and, for each predecessor node connected to said eachordered node: (ii) the corrected RTO of said each predecessor node and(iii) the time delay represented by the edge that directly connects saideach predecessor node to said each ordered node.

As an option not shown in FIG. 2, the process may skip step 210 in casethere is no undefined RTO.

The ‘Estimated RTO’ is calculated in step 210 by traversing theresources as sorted during the topological sort step in the reverseorder, and is calculated for each resource R (as illustrated in FIG. 6).If a resource R has a positive infinite value as ‘Corrected RTO’, it isset to a negative infinite value, the ‘Estimated RTO’ flag is set totrue and the estimated RTO becomes the maximum value X_(i) calculated infunction of all resources where i denotes a given a resource being thetarget of a dependency (R, R_(i)) (meaning for all outgoingdependencies) and R's ‘Corrected RTO’, wherein X_(i) is the differenceof the R_(i) ‘Corrected RTO’ and the time delay d_(i) of the edgebetween R and R_(i). Otherwise, the resource with a finite ‘CorrectedRTO’ is skipped and no ‘Estimate RTO’ is calculated. The negativeinfinite value will be represented as the minimum number that theattribute that represents the RTO can get. Often the computer languageoffers a literal called MIN_VALUE for a given numerical type.

As step 208 has already been run when step 210 is performed, allresources RTO CRON expressions are already converted. If the time delayis a CRON expression, the literal value is equal to the differencebetween the ‘Corrected RTO’ of the dependency target resource and thenext date generated by the CRON expression using the simulation date asbase date. This gives the deadline to activate the resource; otherwisesynchronization will be missed between resources.

Thus in step 210, which is performed after the corrected RTO is computedin step 208 for each ordered node, an estimated RTO is calculated as acorrected RTO for each ordered node remaining as an undefined RTO node.The estimated RTO is calculated as a function of: (a) the corrected RTOof each successor node of each remaining undefined RTO node; and (b) thetime delay represented by the edge that directly connects each remainingundefined RTO node to said each successor node.

While a method to calculate an Estimated RTO has been described in oneembodiment, alternative methods to estimate undefined RTO could also beapplied. For example another way to calculate Xi is to set the values toRi without taking into account the time delays di. This is equivalent toset the (R, Ri) dependency time delay to zero and thus to transform theasynchronous dependency to a synchronous one.

The skilled person will appreciate that if some resources still haveundefined ‘Corrected RTO’, the process is partially complete. In thatcase, these resources are placed at the beginning of the final sequence.Similarly, if negative ‘Corrected RTO’ is found for resource having thecurrent state not equal to the target state, the skilled person willinterpret that the constraints provided by the business are too strictor the IT solution design is not optimized because the time delaysbetween resources are too high. This case should then be forwarded tothe business and IT department.

After step 208 and optionally step 210 are performed, the method goes tostep 212 wherein resources are sorted based on their ‘Corrected RTO’. Instep 212, the ordered nodes are reordered in the dependency sequenceaccording to an ascending order of the corrected RTO of the orderednodes to form an activation sequence of the multiple nodes defining atime ordering of activation of the unique resources represented by themultiple nodes

The optimized activation sequence is defined by an ascending sort of theresources regarding their ‘Corrected RTO’. The comparator for operatingthe sort operation may be a conventional numerical comparator, except iftwo resources have the same ‘Corrected RTO’, then the topological sortfound in step 204 is used in the reverse order to determine the finalorder between these two resources. This means that if a resource ‘B’ isplaced after another resource ‘A’ in the topological sort while theyhave the same ‘Corrected RTO’, then resource ‘B’ will come in firstbecause it should be started before resource ‘A’ in order to respect thedependency between them. Resources that have a current state equal tothe target state can be removed from the sequence because no actionshould be taken to bring them to their target state.

Finally in step 214, the results of this process are provided.

FIG. 3 depicts a data-model in the Unified Modeling Language (UML) tostore the graph representation and the results obtained by running theprocess of the present invention. The data-model comprises entities suchas graph 302, resources 304 and dependencies 306. From the relation'sdirection and cardinality, a skilled person would deduce, for example,that a graph 302 contains a set of resources 304 and dependencies 306. Aresource 304 is defined by several parameters as follows:

-   -   a name;    -   an RTO Expression, which can be a literal or a CRON expression;    -   a Corrected RTO, which will contain the calculated RTO regarding        the RTO defined by the business and the time delay on        dependencies;    -   an estimation RTO Boolean flag, which when set o false means        that the corrected RTO value is a real corrected RTO deducted        from the input data (otherwise it is an estimated RTO);    -   a current state, wherein this attribute will define the state of        the resource at the time when this method will be applied and it        is possible that the resource is already at the requested state;    -   a target state, which is the requested state that should be        reached after the activation sequence found by this method is        applied; and    -   a current state time stamp, wherein this represents the date and        time when the resource reaches its current state. This attribute        is used to calculate the ‘corrected RTO’ when the current state        and the target state are identical.        A dependency 306 is defined by several items:    -   a source resource;    -   a target resource;    -   a time delay expression, which can be a literal or a CRON        expression; and    -   a state expression, which will define if a dependency is active        or not depending on the state of its source.        The data-model for the result is shown in the form of:    -   a Group entity 308: a group contains the resources in the order        as calculated by method of the present invention for a given        weakly connected graph;    -   a ResultRun entity 310: as the method is run for multiple        simulation dates, one ResultRun entity represents the run for a        given simulation date; and    -   a Results entity 312: this is a single object which contains all        runs for different simulation dates.

While the previous data-model represents one embodiment, it is to beappreciated that various other implementations could be used forproviding a computer implemented representation of the graph data-model.Moreover, additional attributes/entities could also be added toimplement different algorithms such as cycle detection, weakly connectedgraph discovering; or other useful attributes related to the businesswhere the current invention is applied, for example the owner name of agiven resource.

Going now to FIG. 4, the main components used in one embodiment of thepresent invention are described.

A ‘Graph Processor’ component (402) is the unit from which the calls ofthe different components to operate the process of the present inventionare operated. A ‘Sorter’ component (404) is coupled to Graph Processor402 and allows the realization of the topological sort (step 204 of FIG.2) and the ‘Corrected RTO’ sort (step 208 of FIG. 2) operations.

A ‘RTO Calculator’ component (406) is also coupled to Graph Processor402 and allows the calculation of the ‘Corrected RTO’ (step 208 of FIG.2) and the ‘Estimated RTO’ (step 210 of FIG. 2).

A ‘CRON-Time Converter’ component 408 is coupled to the Graph Processorcomponent 402 and allows converting the CRON expression for RTO and timedelay into literal values depending on the simulation date, the current‘Corrected RTO’ of the resource or the source of the dependency for atime delay conversion. This component is called at steps 208 and 210 ofFIG. 2.

FIGS. 7 to 11 exemplify the method of the present invention at differentsteps of the process.

The example defined in FIG. 7 shows several resources R1 to R7 linked bydifferent dependencies. Each dependency is characterized by a timedelay. This example is based on a disaster recovery plan scenario whereall resources have only two states ‘ON’ and ‘OFF’, the current state forall resources is ‘OFF’ and the target state ‘ON’. The state expressionon all dependencies indicates that all dependencies are active. Eachresource has a RTO initially defined by business constraint except R5for which the RTO is unknown and represented by a positive infinitevalue. In this example, R1 has a RTO equal to “1 hour” while R4 has aRTO defined as “Monday, 12:00” and so, for each resource contributing tothe general system to be analyzed.

Each dependency has a time delay, and there are synchronous andasynchronous dependencies. Asynchronous dependencies can be literal orbased on an expression. For example, the time delay of dependencybetween R1 and R3 is zero (synchronous); the time delay of dependencybetween R2 and R4 is equal to “1 hour”, as well as the time delaybetween R6 and R7 (asynchronous literal based), while the time delaybetween R3 and R4 is defined as “Monday 11:00” (asynchronous expressionbased).

As already explained, RTOs and time delays may be expressed as literalvalues or CRON expressions. Moreover, in this example only onesimulation date is defined: Simulation date/time=“Monday 6:00”; but theprocess may be repeated for any number of additional simulation dates.

As previously explained, a pre-requisite step is to remove all cyclesfrom the graph and split the graph in weakly connected graphs as shownby steps 110, 112 and 114 of FIG. 1.

In the example of FIG. 7, two weakly connected graphs are respectivelymade of resources R1 to R5 for the first graph consisting of 5 nodes andof resources R6 and R7 for the second graph consisting of 2 nodes.Generally, the DAG of the present invention consists of at least 2 nodes(e.g., 2 nodes, 3 nodes, 4 nodes, 5 nodes, etc., or at least two nodes,at least 3 nodes, at least 4 nodes, at least 5 nodes, etc.).

The multiple nodes in the first graph of resources to R5 in FIG. 7comprise:

-   -   at least one node not connected to any successor node,    -   at least one node connected to at least two successor nodes,    -   at least one node to which no predecessor node is connected, and    -   at least one node to which at least two predecessor nodes are        connected.

The following description is focused on the first graph composed byresources R1 to R5. As per step 204 of FIG. 2, a topological sort on thegraph is performed. Depending on the algorithm used and the data-modelrepresentation applied, the result of the topological sort may slightlyvary. FIG. 8 exemplifies one representation of a topological sort onresource R1 to R5. By reading this topological sort in the reverseorder, the activation sequence of the resources gives that R4 is to beactivated first, then R3, then R2, then R5 and finally R1. Such sequencenot being optimized for the business objective and the time delay due todependency between resources, an optimization is to be found by runningthe method of the present invention.

If the graph for resources R1 to R5 in FIG. 7 is denoted as a first DAG,then the graph of topologically sorted nodes in FIG. 8 may be denoted asa second DAG depicting the dependency sequence of ordered nodes andcomprising directed paths identifying each two nodes connected by adirected edge in the first DAG of FIG. 7.

FIG. 9 shows the result after the ‘Corrected RTO’ calculation is done asper step 208 of FIG. 2. To achieve this result, each resource R1 to R5in FIG. 7 is analyzed one after the other in the order defined by thetopological sort of FIG. 8 according to the following algorithm forcomputing the corrected RTO for each ordered node in the dependencysequence depicted in FIG. 8.

For each ordered node to which no predecessor node is connected, thecorrected RTO of each said ordered node is set equal to the predefinedRTO of said each ordered node.

For each ordered node to which at least one predecessor node isconnected:

-   -   for each predecessor node of at least one predecessor node, the        method computes a sum of the corrected RTO of each predecessor        node and the time delay represented by the edge that directly        connects each predecessor node to each ordered node, which        computes at least one sum such that each sum of the at least one        sum corresponds to a respective predecessor node of the at least        one predecessor node; and    -   the corrected RTO of each ordered node is set equal to the        minimum of the predefined RTO of said each ordered node and a        minimum sum of the at least one sum.

The preceding algorithm is applied to the example in FIG. 7 as follows.

A ‘Corrected RTO’ attribute is initialized with a positive infinitevalue and an ‘Estimated RTO’ flag is set to false as specified in step206.

Analyzing R1 shows that R1 doesn't have any predecessor. So, the‘Corrected RTO’ of R1 is set to its current RTO.

Next, R5 is analyzed and similarly the ‘Corrected RTO’ of R5 is set toits current RTO.

The ‘Corrected RTO’ of R2 is set to the RTO value of “3 hours” becausethe sum of the ‘Corrected RID’ of R1 (1 hour) and the time delay betweenR1 and R2 (3 hours) is equal to “4 hours” which is greater than thecurrent ‘Corrected RTO’ of R2 (3 hours)

The ‘Corrected RTO’ of R3 is set to “1 hour” because for the dependency(R1, R3), the sum of the ‘Corrected RTO’ of R1 and the time delay isequal to “1 hour”. For the other dependency (R5, R3), the sum of the‘Corrected RTO’ of R5 and the time delay is a positive infinite value.So, the ‘Corrected RTO’ of R3 is set to “1 hour” because it is theminimum value between the current ‘Corrected RTO’ of R3 (2 hours), the(R1, R3) calculation (1 hour), and the positive infinite value providedby the calculation of (R5, R3).

The ‘Corrected RID’ of R4 is initially set to “6 hours” because the CRONexpression is “Monday 12:00 AM” and the simulation date is “Monday 6:00AM”. The time delay CRON expression of (R3, R4) is set to “4 hours”because the simulation date is “Monday 6:00 AM”, but as from the abovecalculation, the process knows that R3 should be ready 1 hour after thesimulation date, meaning on “Monday 7:00 AM”, and as the time delay isset as “Monday 11:00 AM”, the literal time delay becomes “4 hours”. Thesum of the ‘Corrected RTO’ of R3 and the time delay (R3, R4) is thus “1hour+4 hours=5 hours”. The sum of the ‘Corrected RTO’ of R2 and the timedelay (R2, R4) is thus “3 hours+1 hour=4 hours”. The minimum valuebetween these three computed values (R4 initial=6 hours, (R3, R4)=5hours and (R2, R4)=4 hours) is “4 hours” and thus the ‘Corrected RTO’ ofR4 is finally set to “4 hours”.

FIG. 9 shows that R5 still doesn't have a defined RTO. So, step 210 ofthe method of the present invention is run to calculate an ‘EstimatedRTO’ for R5. The graph is traversed following the reverse order definedby the topological sort for calculating the estimated RTO of said eachremaining undefined RTO node comprises according to the followingalgorithm.

For each successor node of at least one successor node of said eachremaining undefined RTO node, a difference is calculated between thecorrected RTO of each successor node and the time delay represent d bythe edge that directly connects each remaining undefined RTO node tosaid each successor node, which calculates at least one difference suchthat each difference of the at least one difference corresponds to arespective successor node of the at least one successor node. Then, theestimated RTO of each remaining undefined RTO node is equal to a maximumdifference of the at least one difference.

The results of applying the preceding algorithm to implement step 210 ofFIG. 2 are depicted in FIG. 10. Resources R4, R3 and R2 are skippedbecause their ‘Corrected RTO’ is already known.

The ‘Corrected RTO’ of R5 is set to “0.5 hour” because R5 has only onesuccessor R3, and the ‘Corrected RTO’ of R3 is “1 hour”, the time delayis “0.5 hour” and the difference between these is equal to “0.5 hour”.In the case when such a resource has multiple successors, then themaximum difference would be taken as becoming the Estimated RTO.

Resource R1 is skipped too because its ‘Corrected RID’ is defined andknown (even if equal to its current RTO).

The final step 212 of FIG. 2 is then applied to the graph of FIG. 10.Step 212 sorts the resources by reordering the resources based on their‘Corrected RID’ in an ascending order. The results are depicted in FIG.11 and show the sequence of activation of resources R1 to R5 accordingto the previous calculated RTOs (R1=1, R2=3, R3=1, R4=4 and R5=0.5). So,in the first position, R5 with a ‘Corrected RTO’ equal to 0.5 hour is tobe activated first. Next, even R1 and R3 have the same ‘Corrected RTO’,the topological sort provides that R3 is after R1 (as shown in FIG. 8);and so in the second position, R3 is to be activated, followed by R1 inthe third position. Afterwards, in the fourth position, R2 is to beactivated, and then finally R4 is to be activated. Thus as shown, thefinal optimized activation sequence for R1 to R5 is: R5, R3, R1, R2 andR4. The preceding activation sequence is graphically represented in FIG.11 as a DAG depicting the multiple nodes in the activation sequence.

The present invention can be implemented on a computer system asdepicted in FIG. 12. The data are entered in the storage via the ‘inputdevice’ (1204). The present invention will load the computer code forimplementing method from the storage (1212) and then read the data fromthe storage (1212). The data and method are stored in the memory (1206).The CPU (1202) will run the method and process the data to realize thepresent invention. The results will be sent to the output device (1208)or to the storage (1212). The present invention thus provides a computerimplemented method or system and can take the form of an entirelyhardware embodiment, an entirely software embodiment or an embodimentcontaining both hardware and software elements. In a preferredembodiment, the invention is implemented in software, which includes butis not limited to firmware, resident software, microcode, etc.

Furthermore, the invention can take the form of a computer programproduct comprising a physically tangible computer-readable storagemedium storing the program code for use by, or in connection with acomputer of the computer system using a computer processor (i.e., CPU1202). For the purposes of this description, a computer-readable storagemedium can be any physically tangible apparatus or device that can storethe program for use by, or in connection with the computer system,apparatus, or device.

The computer-readable storage medium can be an electronic, magnetic,optical, electromagnetic, or semiconductor system (or apparatus ordevice). Examples of a computer-readable medium include a semiconductoror solid state memory, magnetic tape, a removable computer diskette, arandom access memory (RAM), a read-only memory (ROM), a rigid magneticdisk and an optical disk. Current examples of optical disks includecompact disk read only memory (CD-ROM), compact disk-read/write (CD-R/W)and DVD.

The description of the present invention has been presented for purposesof illustration and description, and is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the art. Theembodiment was chosen and described in order to best explain theprinciples of the invention, the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

It has to be appreciated that while the invention has been particularlyshown and described with reference to a preferred embodiment todetermine an activation sequence of a plurality of resources; variouschanges in form and detail may be made therein without departing fromthe spirit, and scope of the invention. Specifically, the presentinvention is well suited and easily applicable by a person skilled inthe art to determine a deactivation sequence of the same plurality orany other plurality of resources.

Also, the time delay for a resource to change from one state another canbe taken into account by subtracting this time delay from the RTO beforeprocessing the graph.

Particularly, while embodiments of the present invention have beendescribed in the Information Technology area where resources are ITresources such as applications, services, and network components, thepresent method may be applied in different industries where an optimizedactivation sequence of resources is mandatory.

While particular embodiments of the present invention have beendescribed herein for purposes of illustration, many modifications andchanges will become apparent to those skilled in the art. Accordingly,the appended claims are intended to encompass all such modifications andchanges as fall within the true spirit and scope of this invention.

What is claimed is:
 1. A method, said method comprising: providing, by aprocessor of a computer system, a first Direct Acyclic Graph (DAG)comprising multiple nodes and multiple directed edges, wherein each nodeof the multiple nodes represents a unique resource and is either apredefined Recovery Time Objective (RTO) node comprising a predefinedRTO denoting a maximum elapsed time that the unique resource ispermitted to remain in its current state or an undefined RTO nodecomprising a positive infinite value, wherein the multiple nodescomprise at least two predefined RTO nodes and at least zero undefinedRTO nodes; said processor topologically sorting the nodes of themultiple nodes in the first DAG to order the multiple nodes in adependency sequence of ordered nodes, such that each node in thedependency sequence whose unique resource has a time dependency on theunique resource of at least one other node in the dependency sequence isplaced in the dependency sequence before each node of the at least oneother node; in traversal of the ordered nodes in the dependencysequence, said processor computing a corrected RTO for each ordered nodein the dependency sequence as a function of (i) the predefined RTO ofsaid each ordered node and, for each predecessor node connected to saideach ordered node: (ii) the corrected RTO of said each predecessor nodeand (iii) the time delay represented by the edge that directly connectssaid each predecessor node to said each ordered node; and said processorreordering the ordered nodes in the dependency sequence according to anascending order of the corrected RTO of the ordered nodes to form anactivation sequence of the multiple nodes defining a time ordering ofactivation of the unique resources represented by the multiple nodes andto yield a second DAG in which the reordered nodes in the activationsequence are geometrically sequenced in a one-dimensional linear path inthe ascending order of the corrected RTO.
 2. The method of claim 1, saidmethod further comprising: after said computing the corrected RTO foreach ordered node, said processor calculating an estimated RTO as acorrected RTO for each ordered node remaining as an undefined RTO node,said estimated RTO calculated as a function of: (a) the corrected RTO ofeach successor node of each remaining undefined RTO node and (b) thetime delay represented by the edge that directly connects each remainingundefined RTO node to said each successor node.
 3. The method of claim2, wherein a directed edge from a first node to a second node in eachpair of successive nodes in the second DAG denotes that the second nodeis to be activated before the first node is activated.
 4. The method ofclaim 2, wherein each directed edge of the multiple directed edgesrepresents a time delay and directly connects two nodes of the multiplenodes in a direction from a predecessor node of the two nodes to asuccessor node of the two nodes, and wherein a predecessor resourcebeing the unique resource represented by the predecessor node has a timedependency on a successor resource being the unique resource representedby the successor node.
 5. The method of claim 4, wherein said computingthe corrected RTO for each ordered node in the dependency sequencecomprises: for each ordered node to which no predecessor node isconnected, setting the corrected RTO of each said ordered node as equalto the predefined RTO of said each ordered node; for each ordered nodeto which at least one predecessor node is connected: for eachpredecessor node of the at least one predecessor node, computing a sumof the corrected RTO of each said predecessor node and the time delayrepresented by the edge that directly connects said each predecessornode to said each ordered node, which computes at least one sum suchthat each sum of the at least one sum corresponds to a respectivepredecessor node of the at least one predecessor node; and setting thecorrected RTO of said each ordered node as equal to the minimum of: thepredefined RTO of said each ordered node and a minimum sum of the atleast one sum.
 6. The method of claim 4, wherein the at least zeroundefined RTO nodes comprise at least one undefined RTO node, andwherein said calculating the estimated RTO of said each remainingundefined RTO node comprises: for each successor node of at least onesuccessor node of said each remaining undefined RTO node, calculating adifference between the corrected RTO of each said successor node and thetime delay represented by the edge that directly connects said eachremaining undefined RTO node to said each successor node, whichcalculates at least one difference such that each difference of the atleast one difference corresponds to a respective successor node of theat least one successor node; and setting the estimated RTO of said eachremaining undefined RTO node as equal to a maximum difference of the atleast one difference.
 7. The method of claim 1, wherein the methodfurther comprises: said processor representing the topologically sortednodes as another DAG depicting the dependency sequence of ordered nodesand comprising directed paths, wherein each directed path in the anotherDAG identifies two nodes in the first DAG connected by a respectivedirected edge in the first DAG.
 8. The method of claim 1, wherein the atleast zero undefined RTO nodes comprise at least one undefined RTO node.9. A computer program product, comprising a computer readable hardwarestorage device having a computer readable program code stored therein,said program code configured to be executed by a processor of a computersystem to implement a method for generating a timing sequence foractivating resources linked through time dependency relationships, saidmethod comprising: providing, by said processor, a first Direct AcyclicGraph (DAG) comprising multiple nodes and multiple directed edges,wherein each node of the multiple nodes represents a unique resource andis either a predefined Recovery Time Objective (RTO) node comprising apredefined RTO denoting a maximum elapsed time that the unique resourceis permitted to remain in its current state or an undefined RTO nodecomprising a positive infinite value, wherein the multiple nodescomprise at least two predefined RTO nodes and at least zero undefinedRTO nodes; said processor topologically sorting the nodes of themultiple nodes in the first DAG to order the multiple nodes in adependency sequence of ordered nodes, such that each node in thedependency sequence whose unique resource has a time dependency on theunique resource of at least one other node in the dependency sequence isplaced in the dependency sequence before each node of the at least oneother node; in traversal of the ordered nodes in the dependencysequence, said processor computing a corrected RTO for each ordered nodein the dependency sequence as a function of (i) the predefined RTO ofsaid each ordered node and, for each predecessor node connected to saideach ordered node: (ii) the corrected RTO of said each predecessor nodeand (iii) the time delay represented by the edge that directly connectssaid each predecessor node to said each ordered node; and said processorreordering the ordered nodes in the dependency sequence according to anascending order of the corrected RTO of the ordered nodes to form anactivation sequence of the multiple nodes defining a time ordering ofactivation of the unique resources represented by the multiple nodes andto yield a second DAG in which the reordered nodes in the activationsequence are geometrically sequenced in a one-dimensional linear path inthe ascending order of the corrected RTO.
 10. The computer programproduct of claim 9, said method further comprising: after said computingthe corrected RTO for each ordered node, said processor calculating anestimated RTO as a corrected RTO for each ordered node remaining as anundefined RTO node, said estimated RTO calculated as a function of: (a)the corrected RTO of each successor node of each remaining undefined RTOnode and (b) the time delay represented by the edge that directlyconnects each remaining undefined RTO node to said each successor node.11. The computer program product of claim 10, wherein a directed edgefrom a first node to a second node in each pair of successive nodes inthe second DAG denotes that the second node is to be activated beforethe first node is activated.
 12. The computer program product of claim10, wherein each directed edge of the multiple directed edges representsa time delay and directly connects two nodes of the multiple nodes in adirection from a predecessor node of the two nodes to a successor nodeof the two nodes, and wherein a predecessor resource being the uniqueresource represented by the predecessor node has a time dependency on asuccessor resource being the unique resource represented by thesuccessor node.
 13. A computer system comprising a processor and acomputer readable memory unit coupled to the processor, said memory unitcontaining program code configured to be executed by the processor toimplement a method for generating a timing sequence for activatingresources linked through time dependency relationships, said methodcomprising: providing, by said processor, a first Direct Acyclic Graph(DAG) comprising multiple nodes and multiple directed edges, whereineach node of the multiple nodes represents a unique resource and iseither a predefined Recovery Time Objective (RTO) node comprising apredefined RTO denoting a maximum elapsed time that the unique resourceis permitted to remain in its current state or an undefined RTO nodecomprising a positive infinite value, wherein the multiple nodescomprise at least two predefined RTO nodes and at least zero undefinedRTO nodes; said processor topologically sorting the nodes of themultiple nodes in the first DAG to order the multiple nodes in adependency sequence of ordered nodes, such that each node in thedependency sequence whose unique resource has a time dependency on theunique resource of at least one other node in the dependency sequence isplaced in the dependency sequence before each node of the at least oneother node; in traversal of the ordered nodes in the dependencysequence, said processor computing a corrected RTO for each ordered nodein the dependency sequence as a function of (i) the predefined RTO ofsaid each ordered node and, for each predecessor node connected to saideach ordered node: (ii) the corrected RTO of said each predecessor nodeand (iii) the time delay represented by the edge that directly connectssaid each predecessor node to said each ordered node; and said processorreordering the ordered nodes in the dependency sequence according to anascending order of the corrected RTO of the ordered nodes to form anactivation sequence of the multiple nodes defining a time ordering ofactivation of the unique resources represented by the multiple nodes andto yield a second DAG in which the reordered nodes in the activationsequence are geometrically sequenced in a one-dimensional linear path inthe ascending order of the corrected RTO.
 14. The computer system ofclaim 13, said method further comprising: after said computing thecorrected RTO for each ordered node, said processor calculating anestimated RTO as a corrected RTO for each ordered node remaining as anundefined RTO node, said estimated RTO calculated as a function of: (a)the corrected RTO of each successor node of each remaining undefined RTOnode and (b) the time delay represented by the edge that directlyconnects each remaining undefined RTO node to said each successor node.15. The computer system of claim 14, wherein a directed edge from afirst node to a second node in each pair of successive nodes in thesecond DAG denotes that the second node is to be activated before thefirst node is activated.
 16. The computer system of claim 14, whereineach directed edge of the multiple directed edges represents a timedelay and directly connects two nodes of the multiple nodes in adirection from a predecessor node of the two nodes to a successor nodeof the two nodes, and wherein a predecessor resource being the uniqueresource represented by the predecessor node has a time dependency on asuccessor resource being the unique resource represented by thesuccessor node.